During basic training one is taught basic steps to take for engine
loss. Generally this is assumed/presumed to be for other than engine
fire. The highest priority one now is, what does it mean when a fighter
blows by you with its gear down, flaps down, tail hook down, speed
brakes deployed...

You will also cover what to do with gear problems (Uh, Mr/Ms CFI, Uh, I
don't see a wheel out my window (assumes hi-wing a/c) -- and the reply
will be, "Nuts! those welds must've broken off again.").

Because basic training is done VFR day, most emergency procedures are
for basic VFR day situations. Let's see, what to do when you get lost,
run out of fuel (you aren't lost until you run out of fuel because
until then you just don't know exactly where you is), have a flat, have
a door blow open, have a seatbelt hanging outside the plane, etc.

At the next level of training, you get into Night VFR. New set of
procedures are taught (if engine out, set up for landing, if you don't
like what you see, turn off landing lights). Landing with dead landing
light, landing with dead radio, loss of vacuum and having to do it all
with the whiskey...

When you start into complex, then you are taught what to do when the
gear doesn't come down. Complex/HiPerf you learn what to do with loss
of power because of prop problems. And all that neat gauge stuff.

Instrument rating includes training for loss of radio, what it means
when that low voltage red light comes on, what it means when the DG is
going one direction and the turn coordinator is doing something
else...., when ATC tells you to contact them upon landing.

Depending on the aircraft you are using and the ground school you go
to, you will cover oxygen problems. Let me see, that was no oxygen and
out go the lights... Window blows open at altitude and your approach
plate is probably going to follow it out of the plane...

The one thing I was taught during basic (primary) training, just before
I went for the PP check ride was, pretend that the CEO of the company
is on the plane. Pretend that they like to drink coffee and they hate
to wear it on their nice clothes. Fly accordingly.
Later,
Steve.T
PP ASEL/Instrument